f(t) = e2t cos 5t S- 2 (s – 2)² + 25 2s + 4 s(s² + 4) %3D Ans. f(t) = (sin t –- cos t)² %3D Ans.

Q: 2. Evaluate: (a) L{t – cos 4t + e-3t sinh at} (b) L{U(t – n) + cos 6t U(t – 1/3)} 2s + 14 (c) L…

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Q: 3. Evaluate: 12x dx (a) J2 2-1)* (b) F sin 20 de o cos 20 (c) L1; x2 dx -1 x+2 (d) S, 2x Vx2 + 2 dx

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Q: Find the solution to the Bernoulli Equation. (3siny - 5x)dx + 2x²cotydy=D0 O x³(siny- x)2 = Csin?y O…

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Q: i) dt (1+t)3 j) S(sin?x cos x)dx x+3 k) S: -dx x2+6x-11

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Q: -) Find the general solution of the DE y(4) + 2y" + y = 3 sin t - 5 cos t Use the method of…

A: We can solve this ordinary differential equation by undetermined coefficient

Q: 1 Vx + 10 — о(х), х — 0 te-2n 10n В. о(1/п), п — о 1 — о(е "), п — sin æ = x- +0(x°), x → 0 3 D. n2…

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Q: 5. eу-2*(1 + x?)dx + сos y dy %3D 0, when x %3D 0, у %3D0 2e2* (сos y - sin y) + еУ(2x? + 2х + 3) %3…

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Q: A particle moves along the x-axis so that at any time t, t 2 0, its acceleration is a(t) = -4…

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Q: 2. Evaluate a. [x'(2x° +5)' dx b. dx V1-7x c. [cos 3xsin 3xdr d. sin* 6x cos 6xdx e. [t* cos(2r'…

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Q: #2. | Ax)dzx, f(x)= (sin z, 0srs a/2 |cosr, n/2< rSA f(x)dxr. f(x): #3.

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Q: 2n X f(p sin()cos(0) p sin ()sin(e) • p cos(o) p'sin (4) f(x, y, z) dV = dp de de Jn/2

A: SPHERICAL COORDINATES : The spherical coordinates are : x=ρsin θcosϕy=ρsin θ sinϕz=ρcosθJ=ρ2sinθ…

Q: f) y= xcos(xln x) g) y= 3(sin 2x – x* }** In. 3x'e** h) y= cosx

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Q: Find the general solution of (1+ cosy)dx - xsin ydy = 0. a. X - sin y - x cos y = C b. x + sin y +…

A: The solution is given as

Q: d²y Find the solution for cos(x) (1+ x²) – 2xy = with the conditions %3D dx2 1+x2 y(1) = -1, y(2) =…

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Q: x'e* cos 3xdx + -dy = 0 Vỹ - 1 %3D

A: In this question, we solve the separable differential equation by direct integral. the differential…

Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

Q: (x²-cos(2x). c. T(x) = x d. T(x) x2. find Q at x = t/4. = 100e-3x + In(4x), k=470, A= 0.01r and x=…

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Q: Find L[e2t+2 + e-2t cos 3t + e2t t sin(2t)] A)+ 4s-8 s+2 s-2 ((s-2)2 +4)2 (s+2)2 +9 e2 B)- s+2 s-4…

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Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m − n)] dx…

A: Let's find.

Q: (d) a sin 0 d0 + (x³ – 2x2 cos 0) dx = 0 - %3D (e) x dy - [y + xy°(1+ ln x)] dx = 0 %3D

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Q: a. Find the General and Particular solution of dy/dx = −8 sin 4x ; y = 6 when x = 0

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Q: Find L[e2t t sin(2t)+ e2t+1 + e²t cos 2t] 2s-4 s+2 A)+ A) s+2 * (s-1)² +4)² (s+2)² +4 45-4 S-2 B) +…

A: Given below an detailed solution

Q: -Зп 3 cos? x sin x dx 3 cos?x sin x dx 4. a. b. 2т f(1 + t*)³ dt F(1 + t*)³ dt 5. a. b. •Vī t(1² +…

A: 4. We have to evaluate the values of   (a). (b)

Q: Find the general solution of (2x + y cos (xy))dx + x cos (xy) dy= 0 Show your solutions on a…

A: Solution

Q: Find the particular solution of (cos x – x sin x + y²) dx + 2xy dy = 0 that satisfies the initial…

A: Make the absolute form and solve this differential equation.

Q: (In a + 12x y cos a + x*y cos x)dx + (8xy cos x + 2x"y sin x)dy = 0, 4 2 y(T) = 1/27 b. y da - a(a?…

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Q: Find the solution to the initial value problem for f(x) = 0 and g(x) = 2 cos 5x. a2. - 00 0, u(x,0)…

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Q: Find the linear approximation to f (t)= cos(2t) at t =1/2. Use the linear approximation to…

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Q: Given: x = 0– sin 0; y = 1– cos 0 d'y Find: dz2 d'y dr? (1-cos 0) CO d²y dr (1-cos e) (1- -cos 0)…

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Q: 3. Solve the DE dy a. = x + 2x dx 3 dy b. dx dy C. = 4 cos 6x - dx 4 dy d. dx %3D x2-1 dy e. dx %3D…

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Q: dy 1 dx 3 1 -sin x 3. Find the general solution of +cos(x)y = -e"sinny-². +-cos(x)y 3

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Q: (a) Find the particular solution of dy, 2y cOS I y(T) = 0 dx

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Q: Q6: Determine a particular solution of the equation dzy +4y 4x2 cos 2x dx2 Using D-operator method

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Q: :- x2 + 10x + 24 dx. 1+ cos2 (x) f(t) = %3D At what value of t does the local max of f(t) occur? t =

A: Given: ft=∫0tx2+10x+241+cos2xdx

Q: df Q4) A) Find dx by using chain rule if f = , u=-1 , x=-1 u+1 B) Evaluate the following integral:…

A: A) To find the derivative of the given function f=u-1u+12 with u=1x2-1

Q: 12) dy dx - = x cos (6x²), y(0) = 7 A) y == sin (u) B) y = sin(6x2) + 12 C) y = sin (6x²) + D) y -…

A: In the question we have to solve the differential equation. Bartleby's guidelines: Please post…

Q: Find . dy dx e 4x, = sin (x + 8y) %3D O In sin (x + 8y) 4e4x -1 S cos (x + Sv) S cos (x + Sv) 4ex -…

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Q: 3. Integrate! 12e dt a) ] 5e041 -0.21 b) c) f- dx 6r dr 3r? .$1+ In 3x² d) [Vcot*0 •csc² 0 do 2+…

A: Using Methods Of Integration

Q: 1. + e*y² = x²y² dy da 2. y + sin x = x³y 3. In x - x²y = xy dy da + cos y tan a

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Q: The

A: This is Linear Differential equation in x. We use method of separation of variables.

Q: Evaluate L{e* (cos at – sin nt s+3 A. (s+3)° – n² (s+3)² - – n² 2 S - 3 (s – 3)° – n² (s-3)° -R 2 2…

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Q: f(x) = |x|, −π<x< T 1-(-1)" a. f(x) = 2 Σ=1 sin nx n (-1)"+1 00 b. f(x) = 1 + ² =1 - 2 πT n² (-1)"-1…

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Q: r5x V2 - cost dt dr 2/2 a) 5/2- cos 5r COs 2r b) 5/2 COs 2r 2/2 COS 5.r 2/2 cos 5r - COS 27 d) 2/2…

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Q: 1 = cos t and f(0) = 4 f(0) + f(0+ 2T) + f(0+ 47) ? If f(t) = cos t what is the exact value of %3D 3…

A: ft=cos t and fθ=-14

Q: f cos(mx) cos(nx) dx is equal to {A} [sin(m + n) + sin(m − n)] dx {B} [sin(m + n) - sin(m - n)] dx A…

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Q: Find the general solution of the nonhomogeneous 2nd order ODE (Use the appropriate method) y" - 4y'…

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Q: 1. f(t) = cos(6t) 2. f(t) = (e^(8t)) cosh(3t) 3. f(t) = (t^2) e^(-4t)

A: Lcos(at)=ss2+a2 Leatcosh (bt) = s-a(s-a)2-b2 Ltneat = n!s-an+1

Q: 3n 2n n S " S"(sin x + cos y)e? dx dy dz 2n 'n A. 2n(e2n + e3™) в. 2п(е2т — езт) c. 2n(e3™ + e2") D.…

A: Given: I=∫2π3π∫π2π∫0πsinx+cosyezdxdydz   We know that; ∫sinxdx=-cosx+C∫cosxdx=sinx+C∫exdx=ex+C And…

Q: Solve the DE X V1-y2 dx – (9+x4) dy=0 A tan-(x2/3) – 2 sin-'(y) =C (B In (9+x4) – 4x2 sin-1 y=C © In…

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